Analysis_Multivariate_Seine
Catarina Pien
5/19/2020
Preparation
Load Packages
Import data
- Fish_ndfa: integrated fish dataset
- Merge flow data into rest of data
- Define variable structures
- Order action phases
Fish_ndfa <- read.csv("R_write/FISH_MAN_allIEPsurveys_20200527.csv")
FlowDesignation <- read.csv("Data/FlowDatesDesignations.csv")
Regions <- read.csv("R_write/Stations_Fish_NDFA_2020-06-08.csv")
# Look at data
head(Fish_ndfa)
str(Fish_ndfa)
# Add variables
Fish_ndfa$Date <- ymd(Fish_ndfa$Date)
Fish_ndfa$Month <- month(Fish_ndfa$Date)
Fish_ndfa$Day <- day(Fish_ndfa$Date)
Fish_ndfa$Year <- ordered(Fish_ndfa$Year)
FlowDesignation$Year <- ordered(FlowDesignation$Year)
FlowDesignation$PreFlowStart <- mdy(FlowDesignation$PreFlowStart)
FlowDesignation$PreFlowEnd <- mdy(FlowDesignation$PreFlowEnd)
FlowDesignation$PostFlowStart <- mdy(FlowDesignation$PostFlowStart)
FlowDesignation$PostFlowEnd <- mdy(FlowDesignation$PostFlowEnd)
# Merge data from FlowDesignation Table (Water Year Type, Flow days and type)
# Filter only Pre-During-Post Flow Action Data.
# We have a during action, and then Pre = 30 days before/Post = 30 days after
Fish_all0 <- inner_join(Fish_ndfa,FlowDesignation, by = "Year")
Fish_all1 <- left_join(Fish_all0, Regions)
Fish_all <- Fish_all1 %>%
mutate(ActionPhase = ifelse(Date > PreFlowStart & Date<PreFlowEnd, "Pre", NA)) %>%
mutate(ActionPhase = replace(ActionPhase, Date > PreFlowEnd & Date < PostFlowStart, "During")) %>%
mutate(ActionPhase = replace(ActionPhase, Date > PostFlowStart & Date < PostFlowEnd, "Post")) %>%
filter(!is.na(ActionPhase)) %>%
select(-c(PreFlowStart:PostFlowEnd)) %>%
arrange(Date, Survey, StationCode, CommonName)
# Order Action Phases
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$ActionPhase <- factor(Fish_all$ActionPhase, levels(Fish_all$ActionPhase)[c(3,1,2)])
# Define variable structures
Fish_all$Date <- ymd(Fish_all$Date)
Fish_all$Month <- ordered(Fish_all$Month)
Fish_all$Year <- ordered(Fish_all$Year)
Fish_all$WYType <- as.factor(Fish_all$WYType)
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$X1 <- NULL
Fish_all$Survey <- as.factor(Fish_all$Survey)
Fish_all$StationCode <- as.factor(Fish_all$StationCode)
str(Fish_all)Plotting Functions
## FUNCTIONS FOR PLOTTING -------------------------------------------------------------
VisPoint <- function(data,y) {
y <- enquo(y)
data %>%
ggplot() +
geom_point(mapping = aes(Date,!! y), size = 2) +
theme_bw() +
scale_colour_manual(values = c("coral3", "lightseagreen"))+
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(colour = "black"),
plot.title = element_text(hjust=0.5),
axis.text = element_text(size = 11),
axis.text.x = element_text(angle = 90, hjust = 1),
axis.title = element_text(size = 12),
legend.text = element_text(size = 11),
legend.position = "bottom")
}
# Boxplots by variable of interest
VisBox <- function(data, x, y) {
x <- enquo(x)
y <- enquo(y)
data %>%
ggplot() +
geom_boxplot(mapping = aes(!! x,!! y), fill = "lightseagreen", colour = "lightgray") +
theme_bw() +
scale_colour_manual(values = c("coral3", "lightseagreen"))+
theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(colour = "black"),
plot.title = element_text(hjust=0.5),
axis.text = element_text(size = 11),
axis.text.x = element_text(angle = 90, hjust = 1),
axis.title = element_text(size = 12),
legend.text = element_text(size = 11))
}
#----------------------------------------------------------------------------------------------------
####################################################################################################Exploration of overall dataset
- Station distribution
- Time span
- Number of fish per survey
- Total counts per survey
- Locations
library(leaflet)
# Look at locations
# Define palette
pal <- colorFactor(c("slateblue", "darkseagreen", "orange", "orangered", "hotpink"), domain = c("DJFMP", "Yolo", "Townet", "EDSM", "FMWT"))
leaflet(Fish_all) %>%
addTiles() %>%
addCircleMarkers(
color = ~pal(Survey),
opacity = 0.5,
lng = ~Longitude,
lat = ~Latitude,
label = ~StationCode) %>%
addLegend(pal = pal,
values = ~Survey,
position = "bottomright")pal2 <- colorFactor(c("violet", "navyblue", "darkseagreen", "orange", "orangered", "hotpink"), domain = c("MiddleSacRiver", "ColusaDrainRCS", "CentralYolo", "LowerYolo", "CacheSloughComples", "LowerSacRiver"))
leaflet(Fish_all)%>%
addTiles() %>%
addCircleMarkers(
color = ~pal2(Region),
opacity = 0.5,
lng = ~Longitude,
lat = ~Latitude,
label = ~paste(StationCode, "Lat:", Latitude, "Long:", Longitude)) %>%
addLegend(pal = pal2,
values = ~Region,
position = "bottomright")# Time span
time <- Fish_all%>%
group_by(Survey, Year) %>%
summarize(sum.count = sum(totalCount))
ggplot(time, aes(x = Survey, y = Year, fill = sum.count)) + geom_tile() + theme_minimal()
# Look at datasets
Fishsp <- Fish_all %>%
group_by(CommonName) %>% summarize(count = n())
Fish_all %>%
plot_ly(x = ~Survey,
y = ~totalCount,
type = "box")Fishsp %>%
plot_ly(x = ~CommonName,
y = ~count,
type = "bar")Seine Data
Data Prep
- Filter to just seine data
- Fill in zeros for unlisted species
- Calculate CPUE
- Organize data the way you want it
# Filter Dataset
Seine <- Fish_all %>% filter(MethodCode == "SEIN" | MethodCode == "BSEIN") %>%
select(-c(23:25))
str(Seine)## 'data.frame': 7188 obs. of 24 variables:
## $ Date : Date, format: "2011-07-26" "2011-07-26" ...
## $ Survey : Factor w/ 5 levels "DJFMP","EDSM",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ StationCode : Factor w/ 536 levels "17-53-SRR01",..: 497 497 497 497 497 529 529 529 529 529 ...
## $ MethodCode : Factor w/ 7 levels "BSEIN","FKTR",..: 6 6 6 6 6 6 6 6 6 6 ...
## $ Secchi : num NA NA NA NA NA NA NA NA NA NA ...
## $ Conductivity : num 33.4 33.4 33.4 33.4 33.4 ...
## $ Turbidity : num NA NA NA NA NA NA NA NA NA NA ...
## $ DO : num 9.18 9.18 9.18 9.18 9.18 6.94 6.94 6.94 6.94 6.94 ...
## $ WaterTemp : num 17 17 17 17 17 23.6 23.6 23.6 23.6 23.6 ...
## $ CommonName : Factor w/ 72 levels "American Shad",..: 7 27 37 45 62 14 25 44 45 53 ...
## $ Year : Ord.factor w/ 9 levels "2011"<"2012"<..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Tow : int NA NA NA NA NA NA NA NA NA NA ...
## $ Depth : num 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 ...
## $ VolumeSampled: num 90 90 90 90 90 48 48 48 48 48 ...
## $ Latitude : num 38.6 38.6 38.6 38.6 38.6 ...
## $ Longitude : num -122 -122 -122 -122 -122 ...
## $ totalCount : int 2 1 2 137 15 1 15 29 34 1 ...
## $ Month : Ord.factor w/ 6 levels "6"<"7"<"8"<"9"<..: 2 2 2 2 2 2 2 2 2 2 ...
## $ Day : int 26 26 26 26 26 26 26 26 26 26 ...
## $ WYType : Factor w/ 4 levels "BN","C","D","W": 4 4 4 4 4 4 4 4 4 4 ...
## $ FlowPulseType: Factor w/ 4 levels "CA","MA-Ag","MA-SR",..: 4 4 4 4 4 4 4 4 4 4 ...
## $ NetFlowDays : int 63 63 63 63 63 63 63 63 63 63 ...
## $ Region : Factor w/ 6 levels "CacheSloughComplex",..: 6 6 6 6 6 6 6 6 6 6 ...
## $ ActionPhase : Factor w/ 3 levels "Pre","During",..: 1 1 1 1 1 1 1 1 1 1 ...### Complete Cases
# For each Date, Survey, StationCode combination, make sure each fish species is represented with
# either positive count or zero.
Seine_completecase <- Seine %>%
group_by(Date, Survey, StationCode, CommonName) %>%
summarize(sum.count = sum(totalCount)) %>%
ungroup() %>%
complete(CommonName, nesting(Date, Survey, StationCode), fill = list(sum.count = 0)) %>%
arrange(Date,Survey, StationCode,CommonName)
### Merge back together with rest of data
# Get distinct samples for looking at Water Quality
Seine_samples <- Seine %>% select(-c(CommonName, totalCount)) %>% distinct()
# Merge
Seine_complete <- left_join(Seine_completecase, Seine_samples, by = c("Date", "Survey", "StationCode"))
# There is a Yolo sample with two volumes... this is why there are more rows of Seine_complete
### Calculate CPUE
# Remove samples with no volume
Seine_CPUE <- Seine_complete %>%
filter(!is.na(VolumeSampled))%>%
mutate(CPUE = round(sum.count/VolumeSampled,2))
### Rearrange columns
Seine_f <- Seine_CPUE[, c("Date", "Year", "Month", "Day", "Survey", "StationCode",
"Latitude", "Longitude","MethodCode",
"WYType", "FlowPulseType", "NetFlowDays","ActionPhase", "Region",
"Secchi", "Turbidity", "Conductivity", "WaterTemp", "DO", "Tow",
"Depth", "VolumeSampled", "CommonName", "sum.count", "CPUE")]
### Mean CPUE
## Calculate means for each species by year-location-actionphase
CPUE_means_seine_phase <- Seine_f %>%
group_by(Year, Survey, StationCode, ActionPhase, CommonName) %>%
summarize(mean.CPUE = mean(CPUE)) Data Exploration
Water Quality
- Simple point plots and histograms, correlation matrix
############ OUTLIERS #################
# Boxplots
WTvis1 <- VisPoint(Seine_samples, WaterTemp)
WTvis2 <- VisBox(Seine_samples, Month, WaterTemp)
WTvis3 <- VisBox(Seine_samples, Year, WaterTemp)
Cvis1 <- VisPoint(Seine_samples, Conductivity)
Cvis2 <- VisBox(Seine_samples, Month, Conductivity)
Cvis3 <- VisBox(Seine_samples, Year, Conductivity)
Svis1 <- VisPoint(Seine_samples, Secchi)
Svis2 <- VisBox(Seine_samples, Month, Secchi)
Svis3 <- VisBox(Seine_samples, Year, Secchi)
Tvis1 <- VisPoint(Seine_samples, Turbidity)
Tvis2 <- VisBox(Seine_samples, Month, Turbidity)
Tvis3 <- VisBox(Seine_samples, Year, Turbidity)
DOvis1 <- VisPoint(Seine_samples, DO)
DOvis2 <- VisBox(Seine_samples, Month, DO)
DOvis3 <- VisBox(Seine_samples, Year, DO)
# Plot together
grid.arrange(WTvis1, WTvis2, WTvis3, Cvis1, Cvis2, Cvis3, Svis1, Svis2, Svis3,
Tvis1, Tvis2, Tvis3, DOvis1, DOvis2, DOvis3, ncol = 3)
# Boxplots
plot_ly(data = Seine_samples, x = ~StationCode, y = ~WaterTemp, color = ~Region, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Conductivity, color = ~Region, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Secchi, color = ~Region, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~Turbidity, color = ~Region, type = 'box')plot_ly(data = Seine_samples, x = ~StationCode, y = ~DO, color = ~Region, type = 'box')############ CORRELATIONS ####################
# Correlation Matrix WQ
Corr.wq <- Seine_samples %>% select(WaterTemp, Conductivity, Secchi, Turbidity, DO)
ggpairs(Corr.wq)
# Variance Inflation Factor (VIF)
corvif(Corr.wq) # Want to get rid of the variable if VIF > 4##
##
## Variance inflation factors
##
## GVIF
## WaterTemp 1.108283
## Conductivity 1.688919
## Secchi 1.566020
## Turbidity 1.484982
## DO 1.709443Clean up WQ data (QC)
- Edit anything that needs to be removed, flagged, changed.
- Replace Missing Data
# Clean up wq data
# QC Check - does anything look weird?
Seine_samples %>% filter(WaterTemp>40 | WaterTemp<1)## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2018-10-15 DJFMP LI004E SEIN NA 153.3 16.3 9.17
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 50.6 2018 NA 0.7 63 38.26514 -121.6716 10 15 BN
## FlowPulseType NetFlowDays Region ActionPhase
## 1 MA-Ag 30 CacheSloughComplex PostSeine_samples %>% filter(Secchi > 0.95)## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2011-08-31 Yolo YB BSEIN 1 1157 NA 4.03
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 20.7 2011 1 NA 172.5 38.56538 -121.631 8 31 W
## FlowPulseType NetFlowDays Region ActionPhase
## 1 NF 63 CentralYolo DuringSeine_samples %>% filter(Turbidity > 250) # Slightly sketchy but will leave in## Date Survey StationCode MethodCode Secchi Conductivity Turbidity DO
## 1 2012-08-01 Yolo YB BSEIN 0.12 1409 387 2.08
## 2 2012-10-25 Yolo BL4 BSEIN 0.16 529 254 8.13
## 3 2013-10-21 Yolo YB BSEIN 0.13 1146 288 6.90
## WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1 22.4 2012 1 NA 150.0 38.56538 -121.6310 8 1 BN
## 2 16.2 2012 1 NA 72.5 38.35496 -121.6422 10 25 BN
## 3 14.8 2013 1 NA 100.0 38.56538 -121.6310 10 21 D
## FlowPulseType NetFlowDays Region ActionPhase
## 1 CA 38 CentralYolo Pre
## 2 CA 38 LowerYolo Post
## 3 NF 42 CentralYolo PostSeine_f$WaterTemp[Seine$WaterTemp == 50.6] <- NA # Remove this because really out of range
# Function to fill in missing values with mean
impute.mean <- function(x) replace(x, is.na(x), mean(x, na.rm = TRUE))
# Filling in missing values using impute.mean function from above.
# Variables are renamed because using mutate adds on new columns to the matrix.
# Use impute.mean to fill in NAs, rename updated variables using mutate
Seine_f <- Seine_f %>%
group_by(WYType) %>%
mutate(
Cond = impute.mean(Conductivity),
WTemp = impute.mean(WaterTemp),
SecDepth = impute.mean(Secchi),
Turb = impute.mean(Turbidity),
DOx = impute.mean(DO)) %>%
ungroup()Seine Data Analysis
Preparation
- Filter for species or sets of species
# Lists
list_native <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish")
list_smeltish <- c("Wakasagi", "Inland Silverside")
list_smeltpred <- c("Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass")
list_cyprinid <- c("Sacramento Pikeminnow", "Sacramento Splittail", "Hitch", "Fathead Minnow",
"Golden Shiner", "Hardhead", "Carp", "Goldfish")
list_nmds <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
"Wakasagi", "Inland Silverside", "Delta Smelt",
"Carp", "Goldfish", "Hardhead", "Golden Shiner", "Fathead Minnow", "Hitch",
"Rainwater Killifish", "Western Mosquitofish", "Black Crappie", "White Crappie", "Bluegill", "Bigscale Logperch",
"Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
"Threadfin Shad", "American Shad")
list_nmds_small <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
"Wakasagi", "Inland Silverside", "Delta Smelt", "Longfin Smelt",
"Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
"Threadfin Shad", "American Shad", "Bluegill", "Black Crappie", "Bigscale Logperch")
Seine_tf <- Seine_f %>% filter(CommonName == "Threadfin Shad")
Seine_sucker <- Seine_f %>% filter(CommonName == "Sacramento Sucker")
Seine_lmb <- Seine_f %>% filter(CommonName == "Largemouth Bass")
Seine_black <- Seine_f %>% filter(CommonName == "Sacramento Blackfish")
Seine_pike <- Seine_f %>% filter(CommonName == "Sacramento Pikeminnow")
Seine_natives <- Seine_f %>%filter(CommonName %in% list_native)
Seine_nmds_larger <- Seine_f%>% filter(CommonName %in%list_nmds)
Seine_nmds_0 <- Seine_f %>% filter(CommonName %in% list_nmds_small)- Some summary stats
Summary Stats
snstatsall <- Seine_nmds_larger%>%
group_by(CommonName) %>%
summarize(mean = mean(CPUE),
max = max(CPUE),
min = min(CPUE),
sum = sum(CPUE),
CV = sd(CPUE)/mean,
zeros = sum(CPUE == 0),
n = n(),
prop.absent = round(zeros/n,2))
snstats <- Seine_nmds_0 %>%
group_by(CommonName) %>%
summarize(mean = mean(CPUE),
max = max(CPUE),
min = min(CPUE),
sum = sum(CPUE),
CV = sd(CPUE)/mean,
zeros = sum(CPUE == 0),
n = n(),
prop.absent = round(zeros/n,2))- Remove low abundance, high abundance species. In this case:
- Remove species that are not present: Hardhead, Smallmouth Bass, Longfin Smelt
- Species < 5% of samples: Hitch, Wakasagi, Delta Smelt, Sacramento Blackfish
notabund <- c("Hardhead", "Smallmouth Bass", "Longfin Smelt", "Hitch", "Wakasagi", "Delta Smelt", "Sacramento Blackfish")
Seine_nmds <- filter(Seine_nmds_0, !(CommonName %in% notabund))Exploration/QC
- Look for outliers in species data
- Click species to remove, look at each individual species for any obvious outliers
# Overall CPUE
par(mfrow = c(1,1))
index= seq(1,length(Seine_nmds$CPUE))
# Explore each species - look for outliers here by adding and removing species
Seine_nmds%>%
plot_ly() %>%
add_trace(x = ~index,
y = ~CPUE,
color = ~CommonName,
colors = "Set3",
type = "scatter")ggplot(Seine_nmds,aes(x = Survey, y = CPUE)) + geom_violin() 
- Look at initial trends - environment vs. species
# Threadfin vs environmental
threadfin1 <- ggplot(Seine_tf, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
threadfin2 <- ggplot(Seine_tf, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
threadfin3 <- ggplot(Seine_tf, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
threadfin4 <- ggplot(Seine_tf, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(threadfin1, threadfin2, threadfin3, threadfin4, top = "Threadfin CPUE by Environmental Variable")
# Sac Sucker vs environmental
sucker1 <- ggplot(Seine_sucker, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
sucker2 <- ggplot(Seine_sucker, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
sucker3 <- ggplot(Seine_sucker, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
sucker4 <- ggplot(Seine_sucker, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(sucker1, sucker2, sucker3,sucker4, top = "Sac Sucker CPUE by Environmental Variable")
# Largemouth Bass vs environmental
lmb1 <- ggplot(Seine_lmb, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
lmb2 <- ggplot(Seine_lmb, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
lmb3 <- ggplot(Seine_lmb, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
lmb4 <- ggplot(Seine_lmb, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(lmb1, lmb2, lmb3, lmb4, top = "Largemouth Bass CPUE by Environmental Variable")
Transformations
- Log of sqrt for highly skewed data, or ranging >2 order magnitude
- Arcsine sqrt for proportional data
- Use same transformation for same variable set (e.g. species)
- Consider binary transformation when percent of zero values is high (>50%) or distinct values low (<10)
# Environmental Matrix
Seine_env <- Seine_nmds %>% dplyr::select(c(26:30))
# Check for normality of variables
cond <- Seine_env$Cond
temp <- Seine_env$WTemp
sd <- Seine_env$SecDepth
turb <- Seine_env$Turb
do <- Seine_env$DOx
hist(cond)
hist(log(cond+1)) # Use this
qqnorm(log(cond+1))
hist(temp)
hist(log(temp+1)) # Use this
hist(sqrt(temp))
qqnorm(temp)
qqnorm(log(temp+1))
hist(sd) # Keep it?
hist(log(sd+1))
qqnorm(sd)
qqnorm(log(sd+1))
hist(turb)
hist(sqrt(turb))
hist(log(turb+1))
qqnorm(log(turb+1)) # Use this
hist(do) # Keep it
qqnorm(do)
PCA
Run PCA
- Apply transformations to variables
- If you have variables with different units/scales, choose the correlation matrix (scale = TRUE). Then you do not need to scale your data beforehand.
- Run PCA
- Check PCA (Scree plot, Randomization Tests)
source('biostats.R')
library(vegan)
library(ggfortify)
### Transform to get close to normality assumptions
Seine_env_t <- Seine_env %>% mutate(Cond = log(Cond + 1),
WTemp = log(WTemp + 1),
Turb = log(Turb + 1)) %>%
as.data.frame()
row.names(Seine_env_t) <- row.names(Seine_nmds)
### Run PCA. Center and Scale the data (correlation matrix).
pca.env <- prcomp(Seine_env_t, center=T, scale.=T)
summary(pca.env)## Importance of components:
## PC1 PC2 PC3 PC4 PC5
## Standard deviation 1.2753 1.0883 0.9671 0.8395 0.7409
## Proportion of Variance 0.3253 0.2369 0.1871 0.1409 0.1098
## Cumulative Proportion 0.3253 0.5622 0.7493 0.8902 1.0000### Check how well PCA worked
# Scree Plot with Broken Stick values.
# If eigenvalue is greater than broken stick value it is "significant"
screeplot(pca.env, bstick = TRUE) # According to this, don't keep PC1 and PC2
# Monte Carlo Randomization
# ordi.monte(Seine_env_t, ord = 'pca', dim = 5) # According to this, keep PC1 and PC2
### Check which variables matter
# Loadings. Generally, if magnitude >/= 0.3 this is important.
pca.env$rotation## PC1 PC2 PC3 PC4 PC5
## Cond 0.6304380 -0.0905027 0.1954761 0.1341801 0.7335816
## WTemp 0.3416972 -0.1680611 -0.8754499 0.2677061 -0.1300744
## SecDepth -0.1154881 -0.7468789 0.2948387 0.5583648 -0.1735892
## Turb 0.4559743 0.5028889 0.2947192 0.4583440 -0.4921906
## DOx -0.5143354 0.3909467 -0.1469260 0.6232806 0.4153961# Structure coefficients: linear correlations between original variables and PC scores
pca.structure(pca.env, Seine_env_t, dim = 5, cutoff = 0.4)##
## Structure Correlations:## PC1 PC2 PC3 PC4 PC5
## Cond 0.804 0.544
## WTemp 0.436 -0.847
## SecDepth -0.813 0.469
## Turb 0.582 0.547
## DOx -0.656 0.425 0.523Plot
- Plot and interpret PCA
# Autoplot has best customization, looks nice
# use the "data = " to bring in original dataset so we can
# color-code by factors
autoplot(pca.env, data = Seine_nmds, colour = 'ActionPhase', loadings = TRUE,
loadings.label = TRUE,
loadings.colour = "black",
loadings.label.vjust = -.5,
loadings.label.col = "black",
loadings.label.size = 4,
loadings.label.font = 4) +
theme_bw()
autoplot(pca.env, data = Seine_nmds, colour = 'WYType', loadings = TRUE,
loadings.label = TRUE,
loadings.colour = "black",
loadings.label.vjust = -.5,
loadings.label.col = "black",
loadings.label.size = 4,
loadings.label.font = 4) +
theme_bw()
NMDS
- Pick your variables
- Switch to wide format (species listed across the top)
- Remove any row where nothing was caught
Matrix
Seine_f_sp <- Seine_nmds %>% dplyr::select(c("Survey", "StationCode", "Region", "Date", "FlowPulseType", "WYType",
"ActionPhase", "Month", "CommonName", "CPUE", "Cond",
"WTemp", "SecDepth", "Turb", "DOx"))
# Species Matrix
Seine_sp_w <- Seine_f_sp %>% pivot_wider(names_from = CommonName, values_from = CPUE, values_fill = list(CPUE=0)) %>% ungroup()
# Remove any row where there is no catch for the day.
Seine_sp_sum <- Seine_sp_w %>% mutate(Total = dplyr::select(., 14:25) %>% rowSums(na.rm = TRUE)) %>%
filter(Total !=0)Transform and/or standardize for nMDS
- Some options for transformations: sqrt, log, absence/presence
# Sqrt transform data
sqrt.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
sqrt(x)
})
# Log transform data
log.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
log(x + 1) })
# Absence/Presence data
bin.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
case_when(x>0 ~0,
x ==0 ~1)})# Try binning by month
# Sum data by week
Seine_f_sp$Week <- week(Seine_f_sp$Date)
Seine_f_sp$Year <- year(Seine_f_sp$Date)
Seine_month <- Seine_f_sp %>% group_by(Survey, FlowPulseType, WYType, ActionPhase, Region, StationCode, Year, Month, CommonName) %>%
summarize(mean.CPUE = mean(CPUE),
mean.Cond = mean(Cond),
mean.WTemp = mean(WTemp),
mean.SD = mean(SecDepth),
mean.Turb = mean(Turb),
mean.DO = mean(DOx))
# Species Matrix
Seine_month_w <- Seine_month %>% pivot_wider(names_from = CommonName, values_from = mean.CPUE, values_fill = list(mean.CPUE=0)) %>% ungroup()
# Remove any row where there is no catch for the day.
Seine_month_sum <- Seine_month_w %>% mutate(Total = dplyr::select(., 14:25) %>% rowSums(na.rm = TRUE)) %>%
filter(Total !=0)
# Transform
sqrt.seine2 <- Seine_month_sum %>% mutate_if(is.numeric, function(x) {
sqrt(x)
})Run NMDS
- Run
- Currently a subset of data since otherwise even 2000 iterations won’t converge :(
- Went with sqrt transformation - least change
library(vegan)
test.seine <- sample_n(sqrt.seine, 200)
str(test.seine)
# NMDS Seine
# This can be slow
seine.nmds <- metaMDS(test.seine[,14:25], distance="bray", k=2, trymax=1200, autotransform = FALSE)
seine.nmdsCheck
- Check NMDS
- Stress < 0.15 is acceptable fit.
- Check stressplot.
# Scree Plot - what should k=?
# This can be slow
nmds.scree(test.seine[,14:25], distance='bray', k=5, trymax = 300, autotransform = FALSE) 
### Check NMDS solution
# Large scatter is not good
stressplot(seine.nmds)
Plot
- Plot Results.
- Resources:
- https://jonlefcheck.net/2012/10/24/nmds-tutorial-in-r/
- https://rpubs.com/collnell/manova
- https://chrischizinski.github.io/rstats/vegan-ggplot2/
### NMDS scores
seine.scores <- as.data.frame(scores(seine.nmds))
species.scores <- as.data.frame(scores(seine.nmds, "species"))
species.scores$species <- rownames(species.scores)
# Need a category to merge scores with the rest of env data
row.names(seine.scores) <- row.names(test.seine)
seine.nmdsplot <- cbind(seine.scores, test.seine)
# Prettier Plots
# Option 1
ggplot(seine.nmdsplot, aes(NMDS1, NMDS2, color = ActionPhase)) +
geom_point(position = position_jitter(.1)) +
geom_text(aes(label = WYType)) +
stat_ellipse(type = 't', size = 1) +
annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
theme_minimal() 
# Prettier Plots
# Option 1
ggplot(seine.nmdsplot, aes(NMDS1, NMDS2, color = Region)) +
geom_point(position = position_jitter(.1)) +
geom_text(aes(label = WYType)) +
stat_ellipse(type = 't', size = 1) +
annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
theme_minimal()
# Option 2
# With species scores and boxes
# Make the datasets for the boxes
grp.a <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Pre", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"Pre", c("NMDS1", "NMDS2")]), ] # hull values for grp A
grp.b <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "During", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"During", c("NMDS1", "NMDS2")]), ] # hull values for grp B
grp.c<- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Post", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase ==
"Post", c("NMDS1", "NMDS2")]), ] # hull values for grp C
hull.data0 <- rbind(grp.a, grp.b) #combine grp.a and grp.b
hull.data <- rbind(hull.data0,grp.c)
# Plot
ggplot() +
geom_point(data = seine.nmdsplot, aes(x = NMDS1, y = NMDS2, color = ActionPhase),
position = position_jitter(.1)) +
geom_text(data = seine.nmdsplot, aes(NMDS1, NMDS2, label = WYType, color = ActionPhase)) +
geom_text(data = species.scores, aes(x = NMDS1, y = NMDS2, label= species), color = "black", size = 5) +
theme_minimal() +
annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
geom_polygon(data=hull.data,aes(x=NMDS1,y=NMDS2,fill=ActionPhase,group=ActionPhase),alpha=0.30) 
PERMANOVA
Run models
- Standardize species data (basically becomes proportional data) to reduce influence of large numbers. Could also do sqrt transformation.
- Run PERMANOVA with each variable separately. Only keep significant variables.
- Create model that is significant with greatest R2, move down the list until new variables are not signficant.
- For any categorical variables, test interactions as well.
# Row standardization
seine.st <- data.stand(Seine_sp_sum[,14:25], method = 'total', margin = 'row', plot = F)
# Individual permanova models
(perm.Region <- adonis(formula = seine.st~Region, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 4 42.78 10.6945 54.44 0.11947 0.01 **
## Residuals 1605 315.30 0.1964 0.88053
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.WY <- adonis(formula = seine.st~WYType, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ WYType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## WYType 3 3.09 1.02896 4.6551 0.00862 0.01 **
## Residuals 1606 354.99 0.22104 0.99138
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.WTemp <- adonis(formula = seine.st~WTemp, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ WTemp, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## WTemp 1 3.10 3.09835 14.035 0.00865 0.01 **
## Residuals 1608 354.98 0.22076 0.99135
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Month <- adonis(formula = seine.st~Month, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Month, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Month 5 6.10 1.21925 5.5562 0.01703 0.01 **
## Residuals 1604 351.98 0.21944 0.98297
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Survey <- adonis(formula = seine.st~Survey, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Survey, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Survey 1 29.18 29.1822 142.68 0.0815 0.01 **
## Residuals 1608 328.89 0.2045 0.9185
## Total 1609 358.08 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.WY <- adonis(formula = seine.st~WYType, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ WYType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## WYType 3 3.09 1.02896 4.6551 0.00862 0.01 **
## Residuals 1606 354.99 0.22104 0.99138
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.Action <- adonis(formula = seine.st~ActionPhase, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ ActionPhase, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## ActionPhase 2 2.55 1.27653 5.7701 0.00713 0.01 **
## Residuals 1607 355.52 0.22123 0.99287
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.FlowPulse <- adonis(formula = seine.st~FlowPulseType, data = Seine_sp_sum, method = "bray", permutations = 99))##
## Call:
## adonis(formula = seine.st ~ FlowPulseType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## FlowPulseType 3 2.18 0.72766 3.2836 0.0061 0.01 **
## Residuals 1606 355.89 0.22160 0.9939
## Total 1609 358.08 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Multiple variables
# StationCode, Month, WYType, ActionPhase
(perm.2 <- adonis(formula = seine.st~Region + Month + Region:Month, data = Seine_sp_sum, method = "bray",
permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region + Month + Region:Month, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 4 42.78 10.6945 56.163 0.11947 0.01 **
## Month 5 5.30 1.0594 5.564 0.01479 0.01 **
## Region:Month 20 9.14 0.4568 2.399 0.02552 0.01 **
## Residuals 1580 300.86 0.1904 0.84022
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.3 <- adonis(formula = seine.st~Region*Month + WYType, data = Seine_sp_sum, method = "bray",
permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region * Month + WYType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 4 42.78 10.6945 56.506 0.11947 0.01 **
## Month 5 5.30 1.0594 5.598 0.01479 0.01 **
## WYType 3 2.42 0.8070 4.264 0.00676 0.01 **
## Region:Month 20 9.11 0.4555 2.407 0.02544 0.01 **
## Residuals 1577 298.47 0.1893 0.83353
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.4 <- adonis(formula = seine.st~Region * Month + Region*WYType + ActionPhase, data = Seine_sp_sum, method = "bray",
permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region * Month + Region * WYType + ActionPhase, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 4 42.78 10.6945 57.939 0.11947 0.01 **
## Month 5 5.30 1.0594 5.740 0.01479 0.01 **
## WYType 3 2.42 0.8070 4.372 0.00676 0.01 **
## ActionPhase 2 1.21 0.6051 3.278 0.00338 0.01 **
## Region:Month 20 8.97 0.4486 2.430 0.02506 0.01 **
## Region:WYType 12 8.89 0.7411 4.015 0.02484 0.01 **
## Residuals 1563 288.50 0.1846 0.80571
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1(perm.5 <- adonis(formula = seine.st~Region * Month + Region*WYType + ActionPhase + Region*FlowPulseType, data = Seine_sp_sum, method = "bray",
permutations = 99))##
## Call:
## adonis(formula = seine.st ~ Region * Month + Region * WYType + ActionPhase + Region * FlowPulseType, data = Seine_sp_sum, permutations = 99, method = "bray")
##
## Permutation: free
## Number of permutations: 99
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Region 4 42.78 10.6945 58.562 0.11947 0.01 **
## Month 5 5.30 1.0594 5.801 0.01479 0.01 **
## WYType 3 2.42 0.8070 4.419 0.00676 0.01 **
## ActionPhase 2 1.21 0.6051 3.313 0.00338 0.01 **
## FlowPulseType 3 1.52 0.5074 2.778 0.00425 0.01 **
## Region:Month 20 8.96 0.4482 2.454 0.02504 0.01 **
## Region:WYType 12 8.83 0.7362 4.031 0.02467 0.01 **
## Region:FlowPulseType 12 4.35 0.3627 1.986 0.01216 0.01 **
## Residuals 1548 282.70 0.1826 0.78949
## Total 1609 358.08 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Homogeneity of Variance
- Test for Homogeneity of Variance
- Choose variables in your model
- You want the anova not to be significant (significant means variances are not homogeneous)
- Boxplots should be pretty equal
# Make dissimilarity matrix
spe.d <- vegdist(seine.st, "bray")
# StationCode
(sp.bdp <- betadisper(spe.d, Seine_sp_sum$Region))##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Region)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## CacheSloughComplex CentralYolo LowerSacRiver LowerYolo
## 0.2502 0.3545 0.2174 0.3711
## MiddleSacRiver
## 0.4139
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 4 9.096 2.27412 18.922 3.234e-15 ***
## Residuals 1605 192.890 0.12018
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 4 9.096 2.27412 18.922 999 0.001 ***
## Residuals 1605 192.890 0.12018
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## CacheSloughComplex CentralYolo LowerSacRiver LowerYolo
## CacheSloughComplex 1.0000e-03 2.3000e-01 1.0000e-03
## CentralYolo 2.6781e-06 1.0000e-03 3.9100e-01
## LowerSacRiver 2.6384e-01 1.8360e-08 1.0000e-03
## LowerYolo 6.8259e-07 3.5894e-01 2.1474e-08
## MiddleSacRiver 1.1012e-09 4.4308e-02 1.5893e-07 1.7551e-01
## MiddleSacRiver
## CacheSloughComplex 0.001
## CentralYolo 0.050
## LowerSacRiver 0.001
## LowerYolo 0.184
## MiddleSacRiverplot(sp.bdp, ellipse = TRUE)
boxplot(sp.bdp)
# Month
(sp.bdp2 <- betadisper(spe.d, Seine_sp_sum$Month))##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Month)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## 6 7 8 9 10 11
## 0.5940 0.4078 0.3614 0.3455 0.3889 0.3987
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp2)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 5 2.006 0.40114 3.3466 0.005187 **
## Residuals 1604 192.263 0.11986
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp2,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 5 2.006 0.40114 3.3466 999 0.006 **
## Residuals 1604 192.263 0.11986
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## 6 7 8 9 10 11
## 6 0.00400000 0.00100000 0.00100000 0.00300000 0.010
## 7 0.00589699 0.16800000 0.09000000 0.61600000 0.884
## 8 0.00030353 0.17233564 0.44200000 0.23900000 0.437
## 9 0.00029747 0.08935643 0.46255086 0.09200000 0.285
## 10 0.00403739 0.61937007 0.22506651 0.08158716 0.857
## 11 0.00767118 0.87018153 0.41620055 0.27964219 0.84799411plot(sp.bdp2, ellipse = TRUE)
boxplot(sp.bdp2)
# WYType
sp.bdp3 <- betadisper(spe.d, Seine_sp_sum$WYType)
sp.bdp3##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$WYType)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## BN C D W
## 0.3799 0.3255 0.4120 0.3894
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp3)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 3 1.263 0.42085 3.4755 0.01548 *
## Residuals 1606 194.476 0.12109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp3,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 3 1.263 0.42085 3.4755 999 0.022 *
## Residuals 1606 194.476 0.12109
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## BN C D W
## BN 0.0310000 0.2960000 0.635
## C 0.0306297 0.0130000 0.012
## D 0.3032466 0.0097894 0.440
## W 0.6470484 0.0055393 0.4275720plot(sp.bdp3, ellipse = TRUE)
boxplot(sp.bdp3)
# ActionPhase
sp.bdp4 <- betadisper(spe.d, Seine_sp_sum$ActionPhase)
sp.bdp4##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$ActionPhase)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## Pre During Post
## 0.4138 0.3394 0.3814
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp4)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 2 1.537 0.76831 6.3302 0.001826 **
## Residuals 1607 195.045 0.12137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1permutest(sp.bdp4,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 2 1.537 0.76831 6.3302 999 0.003 **
## Residuals 1607 195.045 0.12137
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## Pre During Post
## Pre 0.00100000 0.154
## During 0.00030026 0.049
## Post 0.15430722 0.04585440plot(sp.bdp4, ellipse = TRUE)
boxplot(sp.bdp4)
# FlowPulseType
sp.bdp5 <- betadisper(spe.d, Seine_sp_sum$FlowPulseType)
sp.bdp5##
## Homogeneity of multivariate dispersions
##
## Call: betadisper(d = spe.d, group = Seine_sp_sum$FlowPulseType)
##
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
##
## Average distance to median:
## CA MA-Ag MA-SR NF
## 0.3982 0.3813 0.4100 0.3582
##
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
## PCoA1 PCoA2 PCoA3 PCoA4 PCoA5 PCoA6 PCoA7 PCoA8
## 142.59 62.00 34.55 25.24 24.39 22.07 19.02 18.54anova(sp.bdp5)## Analysis of Variance Table
##
## Response: Distances
## Df Sum Sq Mean Sq F value Pr(>F)
## Groups 3 0.619 0.20647 1.6972 0.1657
## Residuals 1606 195.367 0.12165permutest(sp.bdp5,pairwise=TRUE)##
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
##
## Response: Distances
## Df Sum Sq Mean Sq F N.Perm Pr(>F)
## Groups 3 0.619 0.20647 1.6972 999 0.159
## Residuals 1606 195.367 0.12165
##
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
## CA MA-Ag MA-SR NF
## CA 0.56200 0.73000 0.063
## MA-Ag 0.56724 0.47000 0.361
## MA-SR 0.72630 0.46347 0.120
## NF 0.06312 0.37808 0.10734plot(sp.bdp5, ellipse = TRUE)
boxplot(sp.bdp5)
CCA
- Format: 1 matrix of predictors, 1 matrix of species data
- Transform and standardize continuous variables
- Transform species data - sqrt
- Check if unimodal distribution. If yes, run CCA.
Run
# Prepare continuous data
seine.env.scaled <- as.data.frame(scale(Seine_sp_sum[,c(9:10, 12:13)]),center = "TRUE", scale = "TRUE")
seine.env.f <- cbind(seine.env.scaled, Seine_sp_sum[,c("Region", "WYType", "ActionPhase", "FlowPulseType", "Month")])
unique(Seine_sp_sum$Region)## [1] MiddleSacRiver CacheSloughComplex LowerSacRiver CentralYolo
## [5] LowerYolo
## 6 Levels: CacheSloughComplex CentralYolo ColusaDrainRCS ... MiddleSacRiver# Prepare species data
seine.sp <- sqrt.seine[,14:25]
# Check unimodal distribution
# Axis length > 4 = unimodal (CCA)
# 2-4 probably unimodal
# <2 = linear model
decorana(seine.sp, ira=0)##
## Call:
## decorana(veg = seine.sp, ira = 0)
##
## Detrended correspondence analysis with 26 segments.
## Rescaling of axes with 4 iterations.
##
## DCA1 DCA2 DCA3 DCA4
## Eigenvalues 0.4822 0.4194 0.2702 0.2582
## Decorana values 0.5982 0.3530 0.2407 0.1847
## Axis lengths 4.4706 5.3601 4.2156 4.3944# Run CCA
spe.cca <- cca(seine.sp ~.,seine.env.f)
summary(spe.cca)##
## Call:
## cca(formula = seine.sp ~ Cond + WTemp + Turb + DOx + Region + WYType + ActionPhase + FlowPulseType + Month, data = seine.env.f)
##
## Partitioning of scaled Chi-square:
## Inertia Proportion
## Total 2.9507 1.000
## Constrained 0.5106 0.173
## Unconstrained 2.4401 0.827
##
## Eigenvalues, and their contribution to the scaled Chi-square
##
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7
## Eigenvalue 0.2629 0.10954 0.05798 0.03001 0.015605 0.013115 0.007742
## Proportion Explained 0.0891 0.03712 0.01965 0.01017 0.005289 0.004445 0.002624
## Cumulative Proportion 0.0891 0.12622 0.14587 0.15604 0.161330 0.165775 0.168398
## CCA8 CCA9 CCA10 CCA11 CA1 CA2
## Eigenvalue 0.007260 0.0028227 0.002296 0.0013393 0.4934 0.3807
## Proportion Explained 0.002461 0.0009566 0.000778 0.0004539 0.1672 0.1290
## Cumulative Proportion 0.170859 0.1718155 0.172593 0.1730474 0.3403 0.4693
## CA3 CA4 CA5 CA6 CA7 CA8 CA9
## Eigenvalue 0.27044 0.24972 0.19435 0.19160 0.18533 0.14996 0.12417
## Proportion Explained 0.09165 0.08463 0.06587 0.06493 0.06281 0.05082 0.04208
## Cumulative Proportion 0.56092 0.64555 0.71142 0.77635 0.83916 0.88999 0.93207
## CA10 CA11
## Eigenvalue 0.11175 0.08869
## Proportion Explained 0.03787 0.03006
## Cumulative Proportion 0.96994 1.00000
##
## Accumulated constrained eigenvalues
## Importance of components:
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6 CCA7
## Eigenvalue 0.2629 0.1095 0.05798 0.03001 0.01561 0.01311 0.007742
## Proportion Explained 0.5149 0.2145 0.11355 0.05877 0.03056 0.02568 0.015161
## Cumulative Proportion 0.5149 0.7294 0.84296 0.90173 0.93229 0.95797 0.973134
## CCA8 CCA9 CCA10 CCA11
## Eigenvalue 0.00726 0.002823 0.002296 0.001339
## Proportion Explained 0.01422 0.005528 0.004496 0.002623
## Cumulative Proportion 0.98735 0.992881 0.997377 1.000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
##
##
## Species scores
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## American Shad -0.3841 -0.20980 -0.58743 -0.03203 -0.08414 0.196517
## Bigscale Logperch 0.9329 0.03495 -0.00828 -0.17376 -0.05012 0.057312
## Black Crappie 1.3219 0.27045 -0.21050 -0.10993 0.17872 -0.172097
## Bluegill 1.2065 0.34274 0.10484 0.37296 0.14234 0.199908
## Inland Silverside -0.2445 -0.09346 0.08654 0.04436 0.01261 -0.018730
## Largemouth Bass 0.2379 0.18258 -0.08157 0.19929 -0.30355 0.139793
## Sacramento Pikeminnow -0.6838 1.07626 -0.32999 -0.05655 -0.11543 -0.004414
## Sacramento Sucker -0.8346 1.67892 -0.30172 -0.16540 0.36727 -0.144164
## Splittail -0.4067 0.54463 -1.40773 0.61095 -0.79030 -0.125964
## Spotted Bass -0.7767 0.82187 0.86054 -0.91506 -0.32607 0.674791
## Striped Bass -0.2743 -0.70523 -0.88603 -0.23782 0.28135 0.275207
## Threadfin Shad 0.5879 -0.07979 -0.05669 -0.23903 -0.07835 -0.140711
##
##
## Site scores (weighted averages of species scores)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## row1 -2.868437 14.3021709 -4.919e+00 -4.600e+00 2.031e+01 -9.368e+00
## row2 -2.343410 8.9632480 -4.922e+00 -1.037e+00 3.192e+00 -5.043e+00
## row3 -2.011955 9.0146711 -4.474e+00 -2.188e+00 8.852e+00 -7.922e+00
## row4 -1.881104 6.7259093 -6.002e+00 1.467e+00 -3.519e+00 -5.208e+00
## row5 -2.349302 10.3776620 -5.060e+00 -1.883e+00 -3.546e-01 -1.966e+00
## row6 -0.879505 0.6757211 3.076e-01 1.771e+00 -2.747e+00 2.651e-01
## row7 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row8 -1.920732 5.9830597 -1.956e+00 -1.195e+00 5.209e+00 -3.809e+00
## row9 0.064454 1.3425657 -3.917e+00 1.622e+00 -6.737e+00 -2.190e+00
## row10 -0.987410 -0.5405630 -5.522e+00 2.517e+00 -7.982e+00 5.858e+00
## row11 -0.939439 -1.3239590 7.861e-02 6.857e-01 2.260e+00 4.611e-01
## row12 -1.016167 0.6456891 -7.349e+00 4.444e+00 -1.310e+01 1.664e+00
## row13 -0.713334 -0.9120108 5.447e-01 5.652e-01 -5.494e-02 -1.103e+00
## row14 -0.859883 1.7233958 -1.905e+00 2.669e+00 -5.041e+00 -9.546e-01
## row15 -1.144787 -3.0688605 -7.974e+00 -2.505e+00 4.482e+00 1.151e+01
## row16 -0.758453 2.2133106 -8.607e+00 6.622e+00 -1.662e+01 -2.748e+00
## row17 -1.027934 0.7003818 3.691e-01 1.377e+00 -1.578e+00 -4.997e-01
## row18 -0.418312 1.6647404 -8.400e+00 -1.284e+00 -7.295e+00 2.158e+00
## row19 -1.362878 5.3958356 -8.656e+00 6.398e+00 -1.488e+01 -3.282e+00
## row20 -2.637254 11.4543680 -3.601e+00 -3.839e+00 1.810e+01 -8.703e+00
## row21 -2.685951 11.1416170 -4.815e+00 -3.096e+00 6.384e+00 -4.922e+00
## row22 -2.260673 12.2670130 -4.353e+00 -2.790e+00 1.391e+01 -6.142e+00
## row23 -1.730341 4.7422562 -1.177e+00 -7.792e-01 5.701e+00 -3.789e+00
## row24 -1.782071 9.0834331 -4.359e+00 -5.168e-01 -2.126e+00 -2.417e-01
## row25 0.236819 -0.4575326 3.726e-01 -4.824e-01 -3.751e+00 -2.359e+00
## row26 2.564791 0.7062283 6.619e-01 1.132e+00 1.194e+00 3.151e+00
## row27 1.954435 0.2175718 4.051e-02 -1.257e+00 7.920e-01 -2.786e+00
## row28 1.718813 0.6232343 7.285e-01 2.686e+00 3.244e+00 8.803e-01
## row29 1.385183 0.5502474 -3.641e-01 2.056e+00 -2.526e-01 -9.660e-02
## row30 1.877202 -0.0243076 -3.312e-01 -1.032e+00 -7.543e-01 -5.905e-01
## row31 1.417876 -0.0227866 -1.928e+00 -1.298e+00 -2.216e+00 -2.930e+00
## row32 2.455298 0.6665579 2.565e-01 3.623e-01 1.878e+00 4.181e-01
## row33 1.792316 0.4082158 -1.033e+00 -2.042e+00 -3.392e-01 -3.060e-01
## row34 1.576917 -0.7486472 -1.647e+00 -3.767e+00 1.358e+00 1.315e+00
## row35 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row36 2.782070 1.7398211 -4.197e+00 5.532e-01 -2.657e-01 -7.300e+00
## row37 -0.641776 -1.2796515 -1.310e+00 -4.718e-01 1.513e-01 9.726e-01
## row38 0.206704 -1.4176096 -2.478e+00 -2.058e+00 4.507e+00 -7.127e-02
## row39 -0.935927 -1.1510555 5.979e-01 9.768e-01 1.727e+00 -2.327e-01
## row40 -0.531499 -0.3124669 -3.727e+00 -4.325e-01 -2.091e+00 9.324e-01
## row41 -0.868069 -0.7280445 -2.895e+00 1.003e+00 -7.864e-01 1.383e+00
## row42 0.003934 -0.8163734 7.640e-01 -1.307e+00 -9.110e-01 -4.171e+00
## row43 -0.792974 -1.0980405 6.296e-01 6.331e-01 1.319e+00 -8.402e-01
## row44 0.109326 0.4024667 -2.019e+00 2.861e+00 -5.614e+00 -1.798e+00
## row45 -0.663046 -1.6475141 -1.148e+00 -7.227e-01 2.771e+00 9.724e-01
## row46 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row47 -1.477664 7.2115196 -4.319e+00 8.469e-01 -1.126e+01 3.186e+00
## row48 -0.194731 0.3907798 -1.569e+00 4.780e-01 -2.504e+00 -2.002e+00
## row49 0.259024 -0.0934723 -1.182e+00 -7.200e-01 -2.522e+00 -3.869e+00
## row50 -0.715416 -0.6109902 -3.579e+00 -1.684e+00 -6.466e-01 2.829e+00
## row51 -1.174648 0.7487793 -6.554e+00 -3.131e+00 3.350e+00 5.243e+00
## row52 -0.621289 0.1424785 -1.942e+00 2.156e+00 -3.492e+00 -1.989e+00
## row53 0.040710 -1.4217528 -2.507e+00 -2.843e+00 -7.684e-01 -1.788e-01
## row54 -0.346232 -1.5096958 -1.929e+00 -1.686e+00 7.429e-01 6.471e-01
## row55 -0.989345 1.1330360 -5.866e+00 2.733e+00 -6.785e+00 -5.564e-01
## row56 -2.612323 11.1636910 -3.705e+00 -3.612e+00 1.580e+01 -7.930e+00
## row57 -0.878520 3.2839702 -1.668e+00 2.043e+00 -8.114e+00 2.703e+00
## row58 -1.058567 -3.8078794 -1.142e+01 -2.650e+00 6.792e+00 1.185e+01
## row59 0.666910 1.0199050 -1.183e+00 -4.691e+00 -4.032e+00 -6.762e+00
## row60 -1.740025 5.6354179 -3.163e+00 4.565e-01 4.208e-01 -3.207e+00
## row61 -1.932632 7.5652800 -2.488e+00 -1.468e+00 7.755e+00 -4.333e+00
## row62 -1.580586 3.8374426 -4.487e-01 -5.482e-01 7.397e+00 -4.201e+00
## row63 -1.751472 8.4923538 -4.470e+00 -1.639e-01 -5.844e+00 9.594e-01
## row64 -1.049858 1.4347994 4.785e+00 -8.495e+00 -5.882e+00 1.168e+01
## row65 -2.847786 12.1938218 -5.482e+00 -3.446e+00 5.920e+00 -4.924e+00
## row66 -2.326511 9.1025303 -2.854e+00 -2.721e+00 1.289e+01 -6.707e+00
## row67 2.081826 2.0682835 -8.376e-01 7.171e+00 -1.041e+01 9.850e+00
## row68 -1.293415 0.7998007 -6.036e+00 2.404e+00 -5.616e+00 8.922e-01
## row69 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row70 -0.734974 5.2333544 -2.590e+00 -1.372e+00 2.667e+00 -4.235e+00
## row71 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row72 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row73 -2.600816 9.8253343 -5.692e+00 -1.885e+00 -7.397e+00 -3.365e-01
## row74 -0.729786 1.6536410 4.329e+00 -6.767e+00 -7.348e+00 1.382e+01
## row75 2.815419 1.0648961 7.612e-01 2.674e+00 1.506e+00 5.502e+00
## row76 2.053373 0.4058797 4.066e-01 4.426e-01 3.759e-01 -1.967e-01
## row77 2.059024 0.4521883 2.541e-01 1.411e+00 1.569e+00 2.228e+00
## row78 1.698775 0.5092343 7.857e-01 2.271e+00 3.880e-01 2.599e+00
## row79 1.735765 0.4729454 7.410e-01 1.952e+00 3.703e-01 2.110e+00
## row80 0.998195 0.1284436 -3.277e+00 1.235e+00 -4.783e+00 3.003e-01
## row81 2.123182 0.4784636 7.548e-01 9.050e-01 9.681e-01 2.718e+00
## row82 2.640949 0.6146211 -2.620e-01 -1.793e+00 -1.201e+00 1.386e+00
## row83 1.351382 -0.5069249 1.912e-01 -3.759e+00 -2.304e+00 -3.250e+00
## row84 2.281856 0.6616946 -1.170e+00 -2.260e+00 2.343e+00 -6.401e+00
## row85 -0.940345 -1.3685623 -5.537e-02 6.106e-01 2.397e+00 6.401e-01
## row86 0.668170 -0.4579716 -4.744e-01 -6.733e-01 1.431e+00 -1.474e+00
## row87 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row88 -0.366123 -1.1160077 -3.505e-01 -4.806e-01 2.381e-01 -3.165e-01
## row89 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row90 -0.244653 -0.6248803 3.820e-01 4.315e-01 7.359e-01 -6.755e-01
## row91 0.019022 -1.3371706 -4.166e+00 -3.733e+00 3.369e+00 4.169e+00
## row92 0.292820 -0.2174486 9.992e-01 1.507e+00 1.836e+00 -1.182e+00
## row93 -0.453974 -1.2147855 -1.301e+00 -1.293e+00 1.960e+00 5.402e-01
## row94 0.748471 -0.7870395 1.831e-01 -3.528e+00 -2.282e+00 -6.359e+00
## row95 -0.768675 1.0683520 -4.959e-02 2.107e+00 -4.465e+00 1.219e+00
## row96 0.026090 0.1396499 -7.820e-03 -2.115e+00 -1.955e+00 -4.576e+00
## row97 -0.922635 1.8191793 -9.780e-02 1.482e+00 -4.574e-01 -2.855e-02
## row98 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row99 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row100 -2.600816 9.8253343 -5.692e+00 -1.885e+00 -7.397e+00 -3.365e-01
## row101 -0.459642 -0.2511058 -8.916e-01 2.663e+00 -5.973e+00 4.291e+00
## row102 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row103 0.320389 3.6240818 -1.951e+00 4.900e+00 -1.329e+01 7.557e+00
## row104 -1.282271 1.3988960 -2.246e-02 7.691e-01 -9.222e-01 -1.198e+00
## row105 -2.782346 11.5662432 -5.537e+00 -3.033e+00 2.391e+00 -3.708e+00
## row106 -2.027838 6.4624348 -2.747e+00 -1.134e+00 9.115e-01 -2.507e+00
## row107 -1.128035 0.4266693 -2.978e+00 7.925e-01 -3.810e+00 4.452e+00
## row108 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row109 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row110 0.604452 0.8388909 -1.294e+00 -3.633e+00 -1.342e-01 -2.467e+00
## row111 -1.336023 1.9746895 1.203e-01 3.480e-01 3.085e+00 -2.559e+00
## row112 0.013478 -0.6683260 1.760e-01 -2.829e-01 -1.033e+00 -5.900e-01
## row113 -0.902374 -0.9678650 -3.718e+00 -8.090e-01 -1.393e+00 4.303e+00
## row114 -0.619560 -0.5599020 -3.706e+00 3.341e-01 -3.364e+00 3.768e+00
## row115 -0.607627 -1.2400755 -3.379e+00 -1.068e+00 -2.540e+00 3.325e+00
## row116 -0.892057 -0.2299380 -3.507e+00 1.145e+00 -4.201e+00 1.973e+00
## row117 -0.292399 -2.1147498 -4.841e+00 -3.176e+00 1.289e+00 4.141e+00
## row118 -0.208557 -0.3894484 -3.932e+00 1.014e+00 -3.376e+00 3.401e+00
## row119 -0.330782 -1.0663146 -1.712e+00 -1.248e+00 -1.927e+00 1.888e-01
## row120 1.631146 0.5251736 -3.122e-02 1.675e+00 -1.149e+00 1.560e+00
## row121 0.995978 -0.1448842 3.726e-01 5.812e-01 8.331e-01 2.276e-01
## row122 1.158954 -0.4032098 4.299e-02 -1.691e+00 -1.550e-01 -2.538e+00
## row123 1.265882 -0.1967685 2.690e-01 -1.650e+00 -9.161e-02 -3.288e+00
## row124 1.181251 -0.2634729 -1.164e-01 -1.001e+00 1.251e-01 -1.856e+00
## row125 1.160073 0.0214436 -1.290e+00 3.156e-01 -1.458e+00 -1.031e+00
## row126 1.764373 0.3017129 7.970e-01 8.609e-01 8.705e-01 1.736e+00
## row127 2.883371 0.3568217 2.175e-01 -2.909e+00 -1.427e+00 3.061e+00
## row128 0.928479 -0.5116043 5.435e-01 -2.424e+00 -1.475e+00 -1.780e+00
## row129 2.482252 1.4129468 -3.602e+00 6.927e-01 -3.116e+00 -5.501e+00
## row130 -1.012822 -1.4489596 -1.469e+00 3.699e-01 1.328e+00 2.652e+00
## row131 -0.405845 -0.6551936 1.057e+00 6.406e-01 1.085e+00 -2.634e+00
## row132 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row133 -0.381036 -0.8748223 5.999e-01 1.929e-01 2.673e-02 -8.154e-01
## row134 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row135 -0.429693 -0.1793167 8.527e-01 -3.015e-01 7.520e-01 -2.792e+00
## row136 0.240445 -0.5944866 -6.399e-01 4.034e-01 6.949e-01 4.874e-01
## row137 -0.694916 -1.5058894 -6.911e-01 -3.782e-01 2.394e+00 5.007e-01
## row138 0.343854 -0.7147327 -3.487e-01 -1.913e+00 -3.047e+00 -3.142e+00
## row139 -0.568266 0.5472482 7.222e-01 2.266e+00 -2.844e-01 5.410e-01
## row140 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
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## row1485 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1486 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1487 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1488 0.833935 2.3310874 -2.344e+00 -6.203e+00 -5.710e+00 -7.716e+00
## row1489 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1490 -1.390913 1.0497653 4.533e+00 -5.803e+00 -4.134e+00 1.061e+01
## row1491 2.213322 6.8617688 -3.376e-01 6.939e+00 1.353e+01 7.214e+00
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## row1494 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row1495 1.332391 1.4338280 2.903e+00 -1.271e+01 -8.298e+00 7.280e+00
## row1496 1.002186 2.6370563 6.734e-01 -1.034e+01 -3.096e+00 -4.980e-01
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## row1498 -1.160509 0.6207489 5.011e-01 1.014e+00 -3.243e-01 -1.278e+00
## row1499 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1500 -3.064432 11.4149750 4.819e+00 -1.800e+01 1.320e+00 2.023e+01
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## row1504 -0.060139 -0.4611052 9.954e-01 7.228e-01 -1.473e+00 4.807e-01
## row1505 0.990291 0.1865734 7.100e-01 1.474e+00 -2.209e+00 3.362e+00
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## row1507 0.750136 -0.3988460 2.733e-01 -1.705e+00 -1.605e+00 -3.208e+00
## row1508 2.074443 0.1670682 -5.458e-01 -3.349e+00 9.840e-01 -4.785e+00
## row1509 1.334000 0.4650468 -6.520e-01 2.967e+00 -1.528e+00 7.205e+00
## row1510 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1511 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
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## row1513 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1514 -1.437665 0.5809849 -1.694e+01 5.017e+00 -1.442e+01 4.522e+00
## row1515 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1516 -0.169885 0.1906313 2.916e-01 3.617e+00 -7.584e+00 3.579e+00
## row1517 -2.440725 10.0414622 -1.173e+01 4.321e+00 -1.150e+01 -6.978e+00
## row1518 -1.075772 -1.7091596 -3.554e+00 -9.618e-01 3.666e+00 5.024e+00
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## row1520 -0.571737 -0.3612858 9.267e-01 2.486e+00 -3.146e+00 9.312e-01
## row1521 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1522 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1523 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row1524 2.875629 0.6437722 6.406e-02 -7.430e-01 6.313e-01 -2.763e-01
## row1525 2.179511 0.7028569 6.083e-01 1.874e+00 -2.031e-01 3.623e+00
## row1526 1.658590 0.2428638 4.910e-01 3.465e-01 -1.094e+00 9.130e-01
## row1527 1.064576 0.0438314 9.743e-01 1.428e+00 1.118e+00 3.949e-01
## row1528 1.101840 -0.4516482 3.580e-01 -2.343e+00 -1.413e+00 -3.687e+00
## row1529 1.376166 -0.0765522 2.247e-01 -1.572e+00 4.497e-01 -2.546e+00
## row1530 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1531 -0.263670 4.3862990 -2.835e+00 3.799e+00 -1.543e+01 6.994e+00
## row1532 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1533 -2.954368 7.5029137 1.484e+01 -3.050e+01 -2.090e+01 5.145e+01
## row1534 -0.966223 -2.6424499 -3.882e+00 -1.534e+00 6.326e+00 5.752e+00
## row1535 2.048900 0.7444202 -8.768e-01 2.161e-01 2.094e+00 -1.886e+00
## row1536 -3.130366 14.9038284 -5.242e+00 -5.233e+00 2.116e+01 -1.017e+01
## row1537 -1.070599 6.2641938 -3.821e+00 1.837e+00 -1.266e+01 4.463e+00
## row1538 -1.238369 2.0594259 -1.139e+01 1.092e+01 -2.492e+01 -5.516e+00
## row1539 -1.461156 -1.9153196 -1.013e+01 -1.067e+00 -5.392e+00 1.498e+01
## row1540 2.268885 0.2799341 -6.998e-01 -2.229e+00 -6.165e+00 -2.843e+00
## row1541 1.448594 -0.4125983 -2.633e-01 -3.726e+00 -2.705e+00 -6.320e+00
## row1542 1.682070 -0.1379373 2.703e-01 -1.971e+00 -1.062e+00 -2.722e+00
## row1543 1.093219 -0.2407756 3.801e-01 -1.413e+00 1.688e-02 -2.839e+00
## row1544 0.580040 -0.2769336 6.506e-01 -6.185e-02 1.029e+00 -2.534e+00
## row1545 1.078620 -0.2903607 6.109e-01 -1.158e+00 -6.113e-01 -1.628e+00
## row1546 0.651379 -0.3736384 3.376e-01 -1.389e+00 6.228e-01 -4.076e+00
## row1547 1.837190 0.5591021 -1.271e-01 2.641e-01 3.717e+00 -3.436e+00
## row1548 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1549 -1.091146 -2.2341875 -4.860e+00 -1.045e+00 2.590e+00 7.289e+00
## row1550 -0.990303 -0.9739745 1.705e-01 1.189e+00 1.030e-01 4.386e-01
## row1551 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1552 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1553 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row1554 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1555 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1556 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1557 1.879387 0.2173697 -1.825e-01 -1.472e+00 -5.776e-01 -3.031e+00
## row1558 2.076800 0.6598185 4.157e-01 1.515e+00 7.063e-01 1.650e+00
## row1559 2.222174 0.5734957 -4.935e-01 -8.838e-01 -1.215e+00 -2.058e+00
## row1560 1.682151 0.0150597 -1.129e-02 -1.786e+00 3.817e-01 -4.135e+00
## row1561 0.794123 -0.3330380 5.477e-01 -9.007e-01 1.078e-01 -2.849e+00
## row1562 1.342752 -0.1652293 -1.772e-01 -2.657e+00 5.465e-01 -5.320e+00
## row1563 2.239321 0.8356637 -4.395e-01 2.637e-01 2.199e+00 -2.099e+00
## row1564 -2.387516 10.6638313 -5.050e+00 -2.081e+00 1.148e+00 -2.505e+00
## row1565 -0.822957 -0.7063200 1.324e+00 1.779e+00 -3.724e-01 -7.238e-01
## row1566 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1567 -1.172319 0.8944728 7.694e-01 7.233e-01 3.263e+00 -2.461e+00
## row1568 0.904903 1.6667813 -1.407e+00 6.641e+00 -1.945e+01 1.066e+01
## row1569 -1.020463 -1.0342700 -4.894e-01 1.044e+00 -2.489e-01 1.370e+00
## row1570 -2.600816 9.8253343 -5.692e+00 -1.885e+00 -7.397e+00 -3.365e-01
## row1571 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1572 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1573 -1.649000 4.3306037 -6.528e-01 -7.612e-01 8.090e+00 -4.492e+00
## row1574 1.974731 0.6555433 6.127e-01 2.319e+00 -7.219e-02 2.489e+00
## row1575 2.650676 0.9558043 5.415e-01 2.237e+00 2.544e-01 4.115e+00
## row1576 2.085863 0.9208571 6.912e-01 3.077e+00 4.147e+00 2.727e+00
## row1577 0.422327 -0.0939740 1.304e+00 2.585e+00 1.783e+00 7.656e-01
## row1578 1.323436 -0.1208932 7.134e-01 -9.024e-01 -3.791e-01 6.186e-01
## row1579 1.432875 0.2814419 -2.333e-01 -1.031e+00 3.370e+00 -4.052e+00
## row1580 1.624256 0.3796275 -6.174e-01 -2.586e-01 -7.132e-01 1.411e+00
## row1581 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1582 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1583 -1.449465 0.5173524 -7.434e+00 2.052e-01 -3.645e+00 5.735e+00
## row1584 -2.784610 11.5879544 -5.535e+00 -3.047e+00 2.513e+00 -3.750e+00
## row1585 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1586 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1587 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1588 -3.174495 15.3270363 -5.204e+00 -5.512e+00 2.354e+01 -1.099e+01
## row1589 -2.851223 12.2267814 -5.479e+00 -3.468e+00 6.105e+00 -4.988e+00
## row1590 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1591 -1.770282 7.6806252 4.346e+00 -1.198e+01 -8.757e+00 2.192e+01
## row1592 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1593 -1.277617 0.5821377 3.786e+00 -4.014e+00 -2.920e+00 7.655e+00
## row1594 2.529849 1.1889610 9.750e-01 4.339e+00 1.803e+00 6.886e+00
## row1595 2.258228 0.3954354 -8.979e-01 1.195e+00 -5.225e-01 7.178e+00
## row1596 1.356499 0.0355543 6.311e-02 -1.273e+00 -5.145e+00 1.577e+00
## row1597 2.478891 1.0250246 2.533e-04 1.369e+00 1.947e+00 2.033e+00
## row1598 0.850862 -0.1915880 -2.958e-01 7.021e-01 1.209e+00 1.415e+00
## row1599 1.079509 0.5147477 -4.538e-01 8.596e-01 5.068e-01 -2.778e+00
## row1600 1.523951 0.5870463 -4.092e-02 1.307e+00 1.459e+00 -1.478e+00
## row1601 -2.805961 11.7927143 -5.517e+00 -3.182e+00 3.664e+00 -4.147e+00
## row1602 2.236166 -0.7284261 -9.777e-01 -7.966e+00 -5.021e+00 -1.073e+01
## row1603 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1604 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1605 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1606 -0.729476 -0.8452689 1.336e+00 8.806e-01 4.393e-01 -2.017e+00
## row1607 -0.929875 -0.8531644 1.493e+00 1.478e+00 8.082e-01 -1.428e+00
## row1608 -2.817651 11.9048213 -5.507e+00 -3.256e+00 4.295e+00 -4.364e+00
## row1609 3.203200 2.5789053 5.988e-01 1.025e+01 -1.627e+00 1.352e+01
## row1610 -1.901073 6.0400562 -2.350e+00 -3.920e+00 -2.665e+00 6.394e+00
##
##
## Site constraints (linear combinations of constraining variables)
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## row1 -1.251401 3.700973 -2.2893600 0.7763368 0.795118 -1.4754487
## row2 -0.950192 2.909512 -1.7002380 0.1387196 -1.662059 -0.4399573
## row3 -0.990722 2.946211 -1.7340842 0.3013150 -1.358625 -0.5520425
## row4 -1.032209 3.161297 -1.8767683 0.2714965 -0.969070 -0.7488483
## row5 -1.092664 3.315612 -1.9885027 0.4040241 -0.473023 -0.9609675
## row6 -0.902503 3.043271 -1.7467633 -0.2508438 -1.912527 -0.4262596
## row7 -1.066641 3.188038 -1.9033203 0.4145950 -0.713912 -0.8411697
## row8 -0.751396 1.471464 -2.8653195 1.2910721 -1.096636 -0.2674977
## row9 -0.741549 1.220747 -3.0429268 1.0268411 -0.917844 -0.2690855
## row10 -0.692583 1.260685 -2.9827816 0.8430905 -1.325627 -0.1407067
## row11 -0.799496 1.366069 -3.2413505 1.0492412 -0.387465 -0.4708770
## row12 -0.705581 1.162364 -2.8201251 1.1756295 -1.394411 -0.0790343
## row13 -0.765454 1.235810 -3.3196547 0.7832891 -0.517349 -0.3910066
## row14 -0.720257 1.156311 -2.8771536 1.1747456 -1.235591 -0.1313536
## row15 -0.770432 1.063197 -3.5421242 0.5348250 -0.232503 -0.4371834
## row16 -0.675995 0.988077 -2.7935610 1.1008707 -1.602516 0.0481671
## row17 -0.749841 1.436621 -2.8779237 2.2822281 -2.637636 -0.7617069
## row18 -0.745776 1.407816 -2.9231389 2.3016010 -2.762674 -0.6299068
## row19 -0.737108 1.185539 -2.8695291 1.2819688 -1.151433 -0.1577940
## row20 -0.910419 2.578884 -0.6954408 -0.0225880 1.323487 -0.3762280
## row21 -0.762875 2.035073 -0.2989175 -0.1639251 0.067306 0.1811312
## row22 -0.745085 2.058358 -0.3068960 -0.2789854 -0.046873 0.2101728
## row23 -0.750720 2.176782 -0.3828036 -0.3813776 0.042808 0.1460023
## row24 -0.807536 2.299879 -0.4723439 -0.2328500 0.502007 -0.0468257
## row25 -0.725924 2.155055 -0.3506349 -0.4831270 -0.126968 0.1939469
## row26 1.372122 0.770312 -0.1406828 3.4812959 1.598656 0.0009633
## row27 1.479535 0.982743 -0.2322139 2.7071286 0.941718 0.1424659
## row28 1.637808 1.189985 -0.3064592 1.6837925 -0.078223 0.4062651
## row29 1.755499 1.127796 -0.2041650 1.1587523 -0.899089 0.6583314
## row30 1.210733 0.339027 -0.4554701 -0.2132410 -1.098550 -0.5319267
## row31 1.170627 0.646189 -0.6696942 -0.3498043 -0.698573 -0.7409652
## row32 1.143490 0.667219 -0.7864432 -0.2251144 -0.622642 -0.6502904
## row33 1.152905 0.788279 -0.8907574 -0.4020225 -0.678983 -0.6273746
## row34 -0.536746 -0.085273 -1.2126060 1.3508046 0.323136 0.6589906
## row35 1.714457 1.344195 -0.3734998 1.1284680 -0.546019 0.5062517
## row36 1.776564 1.584856 -0.4164715 0.5404706 -0.766827 0.3943586
## row37 -0.456717 -0.094532 -1.6596677 0.2966639 0.207637 0.7025056
## row38 -0.492981 0.286908 -1.9754444 -0.0795956 0.755217 0.3728849
## row39 -0.440181 0.156885 -1.7712381 -0.0136290 0.168196 0.6355958
## row40 -0.542144 0.508534 -2.0017496 0.1093941 1.059885 0.2154055
## row41 -0.506257 0.211996 -1.7854346 0.3136466 0.618574 0.4720295
## row42 -0.480288 0.321130 -1.7547716 0.1376599 0.472190 0.4437274
## row43 -0.473083 0.016475 -2.0742683 -0.2326901 0.717452 0.4911156
## row44 -0.436171 0.276294 -1.9805259 -0.3998862 0.387473 0.4909786
## row45 -0.532827 0.203324 -2.0323220 0.1010830 1.058329 0.3185109
## row46 -0.382948 0.723944 -1.4621166 0.8929327 -2.027540 0.1004316
## row47 -0.470673 0.378889 -1.4877734 0.5078848 0.046609 0.6189554
## row48 -0.529699 0.353012 -1.6754118 0.5675000 0.638788 0.4280587
## row49 -0.491895 -0.020142 -2.0008842 -0.0123482 0.770173 0.4906029
## row50 -0.551412 0.228742 -1.9408021 0.3439526 1.062120 0.3263871
## row51 -0.558024 0.302222 -1.7393821 0.6529851 0.887399 0.3692035
## row52 -0.474062 0.203468 -1.4439954 0.6213999 0.068224 0.6582759
## row53 -0.535872 0.014206 -2.2173326 -0.0782523 1.261962 0.3235841
## row54 -0.512573 -0.284966 -2.3185853 -0.2713247 1.245455 0.4225871
## row55 -0.468127 -0.026764 -1.4549979 0.6381217 0.062559 0.7376934
## row56 -0.931751 2.586863 -0.7066572 0.0755572 1.477750 -0.4294627
## row57 -0.401331 0.752667 -1.4465451 0.9485931 -1.834571 -0.0212416
## row58 -0.465602 0.547227 -1.5013872 1.5178712 -1.681690 0.1984579
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## row1570 -0.924987 1.273678 0.7600154 -0.1472825 1.415128 -1.4214420
## row1571 -0.913772 1.065012 0.7580148 -0.1933353 1.423367 -1.3879444
## row1572 -0.930743 1.089765 0.8091776 -0.0320440 1.479853 -1.4110688
## row1573 -0.903868 1.205324 0.7738050 -0.2644011 1.326626 -1.4035209
## row1574 1.634464 0.582214 0.3997857 1.1756362 0.085136 -0.5448915
## row1575 1.611735 0.596295 0.3835437 1.3028000 0.208124 -0.5646188
## row1576 1.621773 0.693110 0.3404865 1.1879097 0.131379 -0.5494696
## row1577 1.089653 0.124114 0.0299623 -0.4066658 -0.105227 -1.8096797
## row1578 1.067276 0.162292 0.0354980 -0.2881634 0.037308 -1.8694854
## row1579 1.044800 0.209870 0.0961733 -0.0813302 0.106561 -1.8971796
## row1580 1.068814 0.266896 0.1332261 -0.1736259 -0.101196 -1.8461897
## row1581 -0.920484 1.412227 0.8269731 0.7204925 0.927825 -1.0244227
## row1582 -0.941319 1.731575 0.7321396 0.6190391 1.116352 -1.1879404
## row1583 -0.590263 -0.014775 -0.3605336 2.2329052 -1.073649 -0.9398589
## row1584 -0.970933 1.958561 0.6178506 0.5676449 1.387111 -1.3442199
## row1585 -0.743093 1.331716 0.8181236 0.1471142 0.253720 -0.3932692
## row1586 -0.777500 1.342355 0.8078009 0.3143593 0.499076 -0.4793739
## row1587 -0.764363 1.411556 0.7166505 0.1011966 0.483193 -0.4933177
## row1588 -0.727972 1.485930 0.7304509 -0.0678931 0.170694 -0.3904441
## row1589 -0.790127 1.526129 0.6502979 0.1202035 0.704015 -0.6012750
## row1590 -0.534113 -0.371143 -0.3500840 2.4113962 -0.899871 -0.5034731
## row1591 -0.828706 1.399916 0.7364135 0.4389330 0.965022 -0.6835111
## row1592 -0.799409 1.440820 0.6955907 0.2564692 0.734170 -0.5835463
## row1593 -0.492036 -0.069967 -0.4898272 1.9120912 -1.094970 -0.5334597
## row1594 1.606747 0.872660 0.0334823 1.1317777 1.078599 -0.5710628
## row1595 1.548214 0.903997 0.0736971 1.5199669 1.399365 -0.6679359
## row1596 1.540954 0.850545 0.0427331 1.5877967 1.399362 -0.6023569
## row1597 1.047025 0.136492 -0.6412887 -0.6690666 1.238644 -1.8162408
## row1598 1.095857 0.274023 -0.2784808 -0.4187147 0.474323 -1.5720539
## row1599 1.072434 0.321846 -0.1742718 -0.1379258 0.496108 -1.5775000
## row1600 1.061371 0.360214 -0.2076049 -0.1284462 0.589181 -1.6153938
## row1601 -0.825159 1.624341 0.5831033 0.1886883 0.996539 -0.7308656
## row1602 -0.839678 1.704518 0.5280305 0.1418074 1.178875 -0.8398984
## row1603 -0.554276 -0.263959 -0.4377268 2.2926962 -0.577108 -0.7091793
## row1604 -0.532848 -0.165369 -0.4598963 2.2008258 -0.835080 -0.5879565
## row1605 -0.879339 1.462591 0.6664107 0.6357545 1.313651 -0.7880545
## row1606 -0.864020 1.451391 0.6020221 0.4597268 1.281821 -0.7788021
## row1607 -0.900477 1.464642 0.6407136 0.7174860 1.476341 -0.8393563
## row1608 -0.832852 1.552661 0.6065033 0.2789772 1.039934 -0.7245350
## row1609 -0.789182 1.625459 0.6232205 -0.0301668 0.832029 -0.7435758
## row1610 -0.897233 1.203000 0.3035783 0.2986395 1.810651 -0.8636798
##
##
## Biplot scores for constraining variables
##
## CCA1 CCA2 CCA3 CCA4 CCA5 CCA6
## Cond -0.01622 -2.217e-01 0.305433 0.19873 -0.048856 -0.531533
## WTemp 0.14971 -2.967e-01 -0.047200 -0.15007 -0.249300 0.009955
## Turb 0.33742 -2.165e-01 -0.524734 -0.35523 0.273235 0.114477
## DOx -0.33172 -1.635e-01 0.004341 0.31177 0.465708 0.092097
## RegionCentralYolo 0.78537 1.539e-01 0.094192 0.26891 0.084933 0.239225
## RegionLowerSacRiver -0.25068 -2.520e-01 0.060737 0.37607 -0.363712 -0.338186
## RegionLowerYolo 0.42073 -1.141e-01 -0.078493 -0.45145 -0.053678 -0.375798
## RegionMiddleSacRiver -0.49077 6.476e-01 0.397692 -0.29888 0.061272 0.083031
## WYTypeC -0.14200 -3.026e-01 0.343368 -0.02261 -0.048435 -0.077870
## WYTypeD 0.04882 -1.620e-02 0.177518 -0.09412 -0.048858 0.430473
## WYTypeW 0.17545 3.955e-01 -0.348980 0.19599 0.003186 -0.195629
## ActionPhaseDuring 0.02895 -2.170e-01 0.118843 -0.16906 -0.240628 -0.280244
## ActionPhasePost 0.08033 8.979e-02 0.231590 0.15258 0.072452 0.088303
## FlowPulseTypeMA-Ag -0.03180 4.521e-02 0.154092 0.11105 0.049077 -0.208028
## FlowPulseTypeMA-SR -0.01707 -7.922e-02 -0.188030 -0.11714 0.088905 -0.150652
## FlowPulseTypeNF -0.01603 2.731e-02 0.070435 0.11374 -0.181806 0.174955
## Month.L 0.12535 1.733e-02 0.422721 0.09403 -0.008567 0.156314
## Month.Q 0.01557 3.280e-01 -0.201168 0.11994 -0.020164 0.050254
## Month.C -0.06573 3.679e-02 -0.292820 0.10089 0.216847 -0.089553
## Month^4 0.05658 -2.580e-01 0.096481 -0.04920 0.286790 -0.041099
## Month^5 -0.03816 3.913e-05 0.058892 -0.03501 -0.163177 -0.146063
##
##
## Centroids for factor constraints
##
## CCA1 CCA2 CCA3 CCA4 CCA5
## RegionCacheSloughComplex -0.54828 -0.84327 -0.81929 0.152854 0.361920
## RegionCentralYolo 1.62629 0.31863 0.19505 0.556842 0.175872
## RegionLowerSacRiver -0.56791 -0.57099 0.13760 0.851972 -0.823979
## RegionLowerYolo 1.09355 -0.29666 -0.20402 -1.173413 -0.139520
## RegionMiddleSacRiver -0.81841 1.07992 0.66319 -0.498417 0.102177
## WYTypeBN -0.12975 -0.19231 -0.09152 -0.180918 0.107377
## WYTypeC -0.26667 -0.56831 0.64483 -0.042456 -0.090958
## WYTypeD 0.14391 -0.04776 0.52324 -0.277412 -0.144011
## WYTypeW 0.23163 0.52207 -0.46071 0.258737 0.004206
## ActionPhasePre -0.14203 0.19595 -0.45980 0.048906 0.251297
## ActionPhaseDuring 0.03512 -0.26328 0.14418 -0.205105 -0.291927
## ActionPhasePost 0.13900 0.15536 0.40072 0.264007 0.125364
## FlowPulseTypeCA 0.10835 -0.03513 -0.17137 -0.286889 0.215566
## FlowPulseTypeMA-Ag -0.07466 0.10612 0.36171 0.260678 0.115202
## FlowPulseTypeMA-SR -0.05609 -0.26028 -0.61778 -0.384872 0.292099
## FlowPulseTypeNF -0.01485 0.02530 0.06526 0.105379 -0.168437
## Month6 -0.07977 0.88668 -2.94814 -1.240382 -0.267809
## Month7 -0.57065 0.76775 -1.32299 0.190157 -0.673943
## Month8 0.02150 -0.15663 -0.06914 0.002764 0.290058
## Month9 0.02043 -0.28340 0.37132 -0.148613 -0.121739
## Month10 0.08564 0.24960 0.34469 0.015468 -0.436736
## Month11 0.60545 1.17604 0.20663 1.630082 1.940838
## CCA6
## RegionCacheSloughComplex 0.47397
## RegionCentralYolo 0.49537
## RegionLowerSacRiver -0.76615
## RegionLowerYolo -0.97677
## RegionMiddleSacRiver 0.13846
## WYTypeBN -0.01447
## WYTypeC -0.14624
## WYTypeD 1.26884
## WYTypeW -0.25826
## ActionPhasePre 0.28774
## ActionPhaseDuring -0.33999
## ActionPhasePost 0.15279
## FlowPulseTypeCA 0.13312
## FlowPulseTypeMA-Ag -0.48832
## FlowPulseTypeMA-SR -0.49497
## FlowPulseTypeNF 0.16209
## Month6 -0.15591
## Month7 -0.61332
## Month8 0.05398
## Month9 -0.17289
## Month10 0.33727
## Month11 0.33421Interpretation
- Interpretation of CCA axis, terms
- global model
- axis
- terms (order matters)
- Can use a step model to create final CCA model
# Test the significance of the CCA
anova(spe.cca)## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + Turb + DOx + Region + WYType + ActionPhase + FlowPulseType + Month, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Model 21 0.51061 15.824 0.001 ***
## Residual 1588 2.44008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = "axis")## Permutation test for cca under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + Turb + DOx + Region + WYType + ActionPhase + FlowPulseType + Month, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## CCA1 1 0.26291 172.1761 0.001 ***
## CCA2 1 0.10954 71.7371 0.001 ***
## CCA3 1 0.05798 37.9694 0.001 ***
## CCA4 1 0.03001 19.6513 0.001 ***
## CCA5 1 0.01561 10.2197 0.002 **
## CCA6 1 0.01311 8.5888 0.006 **
## CCA7 1 0.00774 5.0699 0.316
## CCA8 1 0.00726 4.7547 0.344
## CCA9 1 0.00282 1.8486 1.000
## CCA10 1 0.00230 1.5034 1.000
## CCA11 1 0.00134 0.8771 1.000
## Residual 1598 2.44008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = "terms")## Permutation test for cca under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + Turb + DOx + Region + WYType + ActionPhase + FlowPulseType + Month, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Cond 1 0.01641 10.6817 0.001 ***
## WTemp 1 0.01817 11.8251 0.001 ***
## Turb 1 0.05226 34.0138 0.001 ***
## DOx 1 0.03553 23.1209 0.001 ***
## Region 4 0.27985 45.5316 0.001 ***
## WYType 3 0.03465 7.5159 0.001 ***
## ActionPhase 2 0.02409 7.8392 0.001 ***
## FlowPulseType 3 0.01952 4.2346 0.001 ***
## Month 5 0.03013 3.9212 0.001 ***
## Residual 1588 2.44008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(spe.cca, by = 'margin')## Permutation test for cca under reduced model
## Marginal effects of terms
## Permutation: free
## Number of permutations: 999
##
## Model: cca(formula = seine.sp ~ Cond + WTemp + Turb + DOx + Region + WYType + ActionPhase + FlowPulseType + Month, data = seine.env.f)
## Df ChiSquare F Pr(>F)
## Cond 1 0.00783 5.0943 0.001 ***
## WTemp 1 0.01321 8.5945 0.001 ***
## Turb 1 0.01156 7.5255 0.001 ***
## DOx 1 0.00963 6.2659 0.001 ***
## Region 4 0.23806 38.7325 0.001 ***
## WYType 3 0.04215 9.1433 0.001 ***
## ActionPhase 2 0.00975 3.1712 0.001 ***
## FlowPulseType 3 0.01677 3.6385 0.001 ***
## Month 5 0.03013 3.9212 0.001 ***
## Residual 1588 2.44008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Forward stepping
cca.step <- ordistep(cca(seine.sp ~ 1, data = seine.env.f), scope = formula(spe.cca),
direction = "forward", pstep = 1000)##
## Start: seine.sp ~ 1
##
## Df AIC F Pr(>F)
## + Region 4 2295.5 55.1280 0.005 **
## + Turb 1 2465.6 31.4198 0.005 **
## + WYType 3 2472.6 9.4504 0.005 **
## + DOx 1 2475.4 21.4291 0.005 **
## + Month 5 2476.2 5.7275 0.005 **
## + WTemp 1 2486.9 9.8683 0.005 **
## + ActionPhase 2 2487.0 5.8779 0.005 **
## + Cond 1 2487.8 8.9946 0.005 **
## + FlowPulseType 3 2493.7 2.3581 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region
##
## Df AIC F Pr(>F)
## + WYType 3 2275.5 8.6752 0.005 **
## + Month 5 2279.5 5.1988 0.005 **
## + Turb 1 2287.7 9.7748 0.005 **
## + ActionPhase 2 2288.2 5.6569 0.005 **
## + Cond 1 2290.4 7.0189 0.005 **
## + DOx 1 2290.9 6.6045 0.005 **
## + WTemp 1 2291.4 6.0071 0.005 **
## + FlowPulseType 3 2293.6 2.6290 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType
##
## Df AIC F Pr(>F)
## + Month 5 2259.9 5.1178 0.005 **
## + ActionPhase 2 2266.3 6.6204 0.005 **
## + Turb 1 2268.2 9.2673 0.005 **
## + FlowPulseType 3 2269.7 3.9241 0.005 **
## + DOx 1 2270.7 6.7945 0.005 **
## + Cond 1 2272.6 4.8704 0.005 **
## + WTemp 1 2273.4 4.0875 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month
##
## Df AIC F Pr(>F)
## + WTemp 1 2252.7 9.2327 0.005 **
## + Turb 1 2253.0 8.8437 0.005 **
## + FlowPulseType 3 2254.3 3.8410 0.005 **
## + DOx 1 2254.4 7.4672 0.005 **
## + Cond 1 2257.1 4.8197 0.005 **
## + ActionPhase 2 2257.7 3.1043 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp
##
## Df AIC F Pr(>F)
## + Turb 1 2245.7 8.8744 0.005 **
## + DOx 1 2247.1 7.5366 0.005 **
## + FlowPulseType 3 2247.2 3.7917 0.005 **
## + Cond 1 2249.8 4.8369 0.005 **
## + ActionPhase 2 2250.2 3.1749 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp + Turb
##
## Df AIC F Pr(>F)
## + DOx 1 2240.7 6.9338 0.005 **
## + FlowPulseType 3 2241.1 3.5050 0.005 **
## + ActionPhase 2 2243.4 3.1403 0.005 **
## + Cond 1 2242.7 4.9486 0.010 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp + Turb + DOx
##
## Df AIC F Pr(>F)
## + FlowPulseType 3 2236.5 3.3842 0.005 **
## + Cond 1 2237.8 4.8634 0.005 **
## + ActionPhase 2 2238.7 2.9762 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp + Turb + DOx + FlowPulseType
##
## Df AIC F Pr(>F)
## + Cond 1 2233.2 5.1849 0.005 **
## + ActionPhase 2 2234.0 3.2152 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp + Turb + DOx + FlowPulseType + Cond
##
## Df AIC F Pr(>F)
## + ActionPhase 2 2230.8 3.1712 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Step: seine.sp ~ Region + WYType + Month + WTemp + Turb + DOx + FlowPulseType + Cond + ActionPhasePlot
- Plot CCA
plot(spe.cca, choices = c(1,2), display = c('wa', 'sp', 'bp'), scaling = 2)
# Plot the CCA
cca.biplot = function(cca){
#find plot dimensions (changed these so all the points would fit)
xmin = min(summary((cca))$species[, 1]) * 1.3
xmax = max(summary((cca))$species[, 1]) * 1.2
ymin = min(summary((cca))$species[, 2]) * 1.3
ymax = max(summary((cca))$species[, 2]) * 1.1
par(bty='l')
# plot(cca,disp='species',scaling=1) #scale to show species the best
plot(summary((cca))$species[, 1], summary((cca))$species[, 2],
type = 'n', xlim = c(xmin, xmax), ylim = c(ymin, ymax),
ylab = 'CA2 (3.7% Variation Explained)', xlab = 'CA1 (8.9% Variation Explained)')
axis(side = 1, lwd = 2)
axis(side = 2, lwd = 2)
box(lwd = 2)
#draw origin lines
segments(-2, 0, 2, 0, lwd = 1, lty = 3)
segments(0, -4, 0, 2, lwd = 1, lty = 3)
#Add species names
text(summary((cca))$species[, 1],summary((cca))$species[, 2], labels = rownames(summary((cca))$species), cex = 0.8)
#define continuous variables possibly used
cont.vars=c('Cond','WTemp','DOx','Turb')
bi.names = row.names(summary(cca)$biplot) #names of environmental variables
# centroid.names=row.names(summary(cca)$centroid)
centroid.names = data.frame(Rows = rownames(summary((cca))$centroid))
#Pain in the a$$ way to do this, but I created abbreviated names for each level of
#my categorical variable so that they would look nicer when plotted
#Else I would have names like HabitatC on the biplot
#
centroid.names$New[centroid.names$Rows == 'ActionPhasePre'] = 'PreAction'
centroid.names$New[centroid.names$Rows == 'ActionPhaseDuring'] = 'DuringAction'
centroid.names$New[centroid.names$Rows == 'ActionPhasePost'] = 'PostAction'
centroid.names$New[centroid.names$Rows == 'WYTypeC'] = 'CriticalWY'
centroid.names$New[centroid.names$Rows == 'WYTypeD'] = 'DryWY'
centroid.names$New[centroid.names$Rows == 'WYTypeW'] = 'WetWY'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-Ag'] = 'AgPulse'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-SR'] = 'SRPulse'
centroid.names$New[centroid.names$Rows == 'FlowPulseTypeNF'] = 'NoFA'
centroid.names$New[centroid.names$Rows == 'Month4'] = 'Apr'
centroid.names$New[centroid.names$Rows == 'Month5'] = 'May'
centroid.names$New[centroid.names$Rows == 'Month6'] = 'June'
centroid.names$New[centroid.names$Rows == 'Month7'] = 'July'
centroid.names$New[centroid.names$Rows == 'Month8'] = 'Aug'
centroid.names$New[centroid.names$Rows == 'Month9'] = 'Sep'
centroid.names$New[centroid.names$Rows == 'Month10'] = 'Oct'
centroid.names$New[centroid.names$Rows == 'Month11'] = 'Nov'
centroid.names$New[centroid.names$Rows == 'Month12'] = 'Dec'
centroid.names$New[centroid.names$Rows == 'Month1'] = 'Jan'
centroid.names$New[centroid.names$Rows == 'Month2'] = 'Feb'
centroid.names$New[centroid.names$Rows == 'Month3'] = 'Mar'
centroid.names$New[centroid.names$Rows == 'RegionCacheSloughComplex'] = 'CacheSloughComplex'
centroid.names$New[centroid.names$Rows == 'RegionCentralYolo'] = 'CentralYolo'
centroid.names$New[centroid.names$Rows == 'RegionColusaDrainRCS'] = 'ColusaDrainRCS'
centroid.names$New[centroid.names$Rows == 'RegionLowerSacRiver'] = 'LowerSacRiver'
centroid.names$New[centroid.names$Rows == 'RegionLowerYolo'] = 'LowerYolo'
centroid.names$New[centroid.names$Rows == 'RegionMiddleSacRiver'] = 'MiddleSacRiver'
#This could possibly be slimmed down, but it plots arrows if the variable is continuous (part of the list above)
# and plots a point for the categorical variables instead
for(i in 1:length(summary(cca)$biplot[, 1])){
#Test that the row name is one of the continuous variables before plotting arrows
if(bi.names[i] %in% cont.vars){
arrows(0, 0, summary(cca)$biplot[i, 1], summary(cca)$biplot[i, 2],
lwd = 1, angle = 25, length = 0.10, col = "#F4aa42")
text(summary(cca)$biplot[i, 1] * 2,
summary(cca)$biplot[i, 2] * 2, labels = bi.names[i], col = '#F4aa42', cex = 0.8, font = 4)
}
}
#now plot the centered mean value of each nominal variable
#Use if statement to test for case where I don't have any categorical variables
if(is.numeric(summary(cca)$centroids) == TRUE){
points(summary(cca)$centroids[, 1] * 0.9, summary(cca)$centroids[, 2] * 0.9, pch = 15, col = 'black')
text(summary(cca)$centroids[, 1] * 0.9, (summary(cca)$centroids[, 2] * 0.9 + 0.15), labels = centroid.names$New,
col = 'darkcyan', cex = 0.7, adj = .5)
}
}
cca.biplot(spe.cca)